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Question Number 25780 Answers: 1 Comments: 0

every periodic function is differentiable.true or false justify

$${every}\:{periodic}\:{function}\:{is}\: \\ $$$${differentiable}.{true}\:{or}\:{false}\:{justify} \\ $$

Question Number 25275 Answers: 0 Comments: 0

Question Number 25103 Answers: 1 Comments: 0

Question Number 25091 Answers: 1 Comments: 0

A particle of mass m moving with speed u collides perfectly inelastically with a sphere of radius R and same mass, at rest, at an impact parameter d. Find (a) Angle between their final velocities (b) Magnitude of their final velocities

$${A}\:{particle}\:{of}\:{mass}\:{m}\:{moving}\:{with} \\ $$$${speed}\:{u}\:{collides}\:{perfectly}\:{inelastically} \\ $$$${with}\:{a}\:{sphere}\:{of}\:{radius}\:{R}\:{and}\:{same} \\ $$$${mass},\:{at}\:{rest},\:{at}\:{an}\:{impact}\:{parameter} \\ $$$${d}.\:{Find} \\ $$$$\left({a}\right)\:{Angle}\:{between}\:{their}\:{final}\:{velocities} \\ $$$$\left({b}\right)\:{Magnitude}\:{of}\:{their}\:{final} \\ $$$${velocities} \\ $$

Question Number 25086 Answers: 0 Comments: 4

Question Number 25058 Answers: 1 Comments: 0

Two objects slide over a frictionless horizontal surface. The first object, mass m_1 = 5 kg, is propelled with a speed u = 4.5 m/s towards the second object, mass m_2 = 5 kg, which is initially at rest. After the collision, both objects have velocities which are directed at θ = 60° on either side of the original line of motion of the first object. What can you say about the elasticity of collision?

$${Two}\:{objects}\:{slide}\:{over}\:{a}\:{frictionless} \\ $$$${horizontal}\:{surface}.\:{The}\:{first}\:{object}, \\ $$$${mass}\:{m}_{\mathrm{1}} \:=\:\mathrm{5}\:{kg},\:{is}\:{propelled}\:{with}\:{a} \\ $$$${speed}\:{u}\:=\:\mathrm{4}.\mathrm{5}\:{m}/{s}\:{towards}\:{the}\:{second} \\ $$$${object},\:{mass}\:{m}_{\mathrm{2}} \:=\:\mathrm{5}\:{kg},\:{which}\:{is} \\ $$$${initially}\:{at}\:{rest}.\:{After}\:{the}\:{collision}, \\ $$$${both}\:{objects}\:{have}\:{velocities}\:{which}\:{are} \\ $$$${directed}\:{at}\:\theta\:=\:\mathrm{60}°\:{on}\:{either}\:{side}\:{of} \\ $$$${the}\:{original}\:{line}\:{of}\:{motion}\:{of}\:{the} \\ $$$${first}\:{object}.\:{What}\:{can}\:{you}\:{say}\:{about} \\ $$$${the}\:{elasticity}\:{of}\:{collision}? \\ $$

Question Number 25038 Answers: 1 Comments: 0

For a particle of a rotating rigid body, v = rω. So (1) ω ∝ (1/r) (2) ω ∝ v (3) v ∝ r (4) ω is independent of r

$$\mathrm{For}\:\mathrm{a}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{a}\:\mathrm{rotating}\:\mathrm{rigid}\:\mathrm{body}, \\ $$$${v}\:=\:{r}\omega.\:\mathrm{So} \\ $$$$\left(\mathrm{1}\right)\:\omega\:\propto\:\left(\mathrm{1}/{r}\right) \\ $$$$\left(\mathrm{2}\right)\:\omega\:\propto\:{v} \\ $$$$\left(\mathrm{3}\right)\:{v}\:\propto\:{r} \\ $$$$\left(\mathrm{4}\right)\:\omega\:\mathrm{is}\:\mathrm{independent}\:\mathrm{of}\:{r} \\ $$

Question Number 25013 Answers: 0 Comments: 3

With reference to figure of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.) (1) The moment of inertia of cube about z-axis is, I_z = I_x + I_y (2) The moment of inertia of cube about z′ is, I_(z′) = I_z + ((ma^2 )/2) (3) The moment of inertia of cube about z′′ is, I_(z′) = I_z + ((ma^2 )/2) (4) I_x = I_y

Question Number 25000 Answers: 1 Comments: 0

find x,y from the equation: (1/2)x−yi+(1/(1+i))=((√(1+ω^8 ))+(√(1+ω^(10) )))^4

$${find}\:{x},{y}\:{from}\:{the}\:{equation}: \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}{x}−{yi}+\frac{\mathrm{1}}{\mathrm{1}+{i}}=\left(\sqrt{\mathrm{1}+\omega^{\mathrm{8}} }+\sqrt{\mathrm{1}+\omega^{\mathrm{10}} }\right)^{\mathrm{4}} \\ $$$$ \\ $$

Question Number 24997 Answers: 0 Comments: 0

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Question Number 24945 Answers: 0 Comments: 4

A particle of mass m moving with a speed v hits elastically another stationary particle of mass 2m on a smooth horizontal circular tube of radius r. The time in which the next collision will take place is equal to

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{a} \\ $$$$\mathrm{speed}\:{v}\:\mathrm{hits}\:\mathrm{elastically}\:\mathrm{another} \\ $$$$\mathrm{stationary}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}{m}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{smooth}\:\mathrm{horizontal}\:\mathrm{circular}\:\mathrm{tube}\:\mathrm{of} \\ $$$$\mathrm{radius}\:{r}.\:\mathrm{The}\:\mathrm{time}\:\mathrm{in}\:\mathrm{which}\:\mathrm{the}\:\mathrm{next} \\ $$$$\mathrm{collision}\:\mathrm{will}\:\mathrm{take}\:\mathrm{place}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 24934 Answers: 0 Comments: 3

A uniform circular disc of mass 1.5 kg and radius 0.5 m is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude F = 0.5 N are applied simultaneously along the three sides of an equilateral triangle xyz with its vertices on the perimeter of the disc. One second after applying the forces, the angular speed of the disc in rad/s is :

$$\mathrm{A}\:\mathrm{uniform}\:\mathrm{circular}\:\mathrm{disc}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}.\mathrm{5}\:\mathrm{kg} \\ $$$$\mathrm{and}\:\mathrm{radius}\:\mathrm{0}.\mathrm{5}\:\mathrm{m}\:\mathrm{is}\:\mathrm{initially}\:\mathrm{at}\:\mathrm{rest}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{horizontal}\:\mathrm{frictionless}\:\mathrm{surface}.\:\mathrm{Three} \\ $$$$\mathrm{forces}\:\mathrm{of}\:\mathrm{equal}\:\mathrm{magnitude}\:{F}\:=\:\mathrm{0}.\mathrm{5}\:\mathrm{N} \\ $$$$\mathrm{are}\:\mathrm{applied}\:\mathrm{simultaneously}\:\mathrm{along}\:\mathrm{the} \\ $$$$\mathrm{three}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle} \\ $$$${xyz}\:\mathrm{with}\:\mathrm{its}\:\mathrm{vertices}\:\mathrm{on}\:\mathrm{the}\:\mathrm{perimeter} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{disc}.\:\mathrm{One}\:\mathrm{second}\:\mathrm{after}\:\mathrm{applying} \\ $$$$\mathrm{the}\:\mathrm{forces},\:\mathrm{the}\:\mathrm{angular}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{disc} \\ $$$$\mathrm{in}\:\mathrm{rad}/\mathrm{s}\:\mathrm{is}\:: \\ $$

Question Number 24909 Answers: 0 Comments: 0

Question Number 24893 Answers: 0 Comments: 2

About a collision which of the following are not correct a. Physical touch is a must b. Particles cannot change c. Effect of external force is not considered d. Momentum may or may not change multi−correct question

$$\mathrm{About}\:\mathrm{a}\:\mathrm{collision}\:\mathrm{which}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{following}\:\mathrm{are}\:\mathrm{not}\:\mathrm{correct} \\ $$$$\mathrm{a}.\:\mathrm{Physical}\:\mathrm{touch}\:\mathrm{is}\:\mathrm{a}\:\mathrm{must} \\ $$$$\mathrm{b}.\:\mathrm{Particles}\:\mathrm{cannot}\:\mathrm{change} \\ $$$$\mathrm{c}.\:\mathrm{Effect}\:\mathrm{of}\:\mathrm{external}\:\mathrm{force}\:\mathrm{is}\:\mathrm{not}\:\mathrm{considered} \\ $$$$\mathrm{d}.\:\mathrm{Momentum}\:\mathrm{may}\:\mathrm{or}\:\mathrm{may}\:\mathrm{not}\:\mathrm{change} \\ $$$$\mathrm{multi}−\mathrm{correct}\:\mathrm{question} \\ $$

Question Number 24879 Answers: 0 Comments: 4

A particle of mass m is fixed to one end of a light rigid rod of length l and rotated in a vertical circular path about its other end. The minimum speed of the particle at its highest point must be

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{fixed}\:\mathrm{to}\:\mathrm{one}\:\mathrm{end} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{light}\:\mathrm{rigid}\:\mathrm{rod}\:\mathrm{of}\:\mathrm{length}\:{l}\:\mathrm{and}\:\mathrm{rotated} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{circular}\:\mathrm{path}\:\mathrm{about}\:\mathrm{its} \\ $$$$\mathrm{other}\:\mathrm{end}.\:\mathrm{The}\:\mathrm{minimum}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{particle}\:\mathrm{at}\:\mathrm{its}\:\mathrm{highest}\:\mathrm{point}\:\mathrm{must}\:\mathrm{be} \\ $$

Question Number 24877 Answers: 0 Comments: 7

Question Number 24858 Answers: 2 Comments: 0

If three positive numbers a, b, c are in A.P. and (1/a^2 ), (1/b^2 ), (1/c^2 ) also in A.P., then (1) a = b = c (2) 2b = 3a + c (3) b^2 = ((ac)/8) (4) 2c = 2b + a

$$\mathrm{If}\:\mathrm{three}\:\mathrm{positive}\:\mathrm{numbers}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{in} \\ $$$$\mathrm{A}.\mathrm{P}.\:\mathrm{and}\:\frac{\mathrm{1}}{{a}^{\mathrm{2}} },\:\frac{\mathrm{1}}{{b}^{\mathrm{2}} },\:\frac{\mathrm{1}}{{c}^{\mathrm{2}} }\:\mathrm{also}\:\mathrm{in}\:\mathrm{A}.\mathrm{P}.,\:\mathrm{then} \\ $$$$\left(\mathrm{1}\right)\:{a}\:=\:{b}\:=\:{c} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}{b}\:=\:\mathrm{3}{a}\:+\:{c} \\ $$$$\left(\mathrm{3}\right)\:{b}^{\mathrm{2}} \:=\:\frac{{ac}}{\mathrm{8}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{2}{c}\:=\:\mathrm{2}{b}\:+\:{a} \\ $$

Question Number 24873 Answers: 0 Comments: 6

A rigid body is made of three identical thin rods, each of length L, fastened together in the form of letter H. The body is free to rotate about a horizontal axis that runs along the length of one of legs of H. The body is allowed to fall from rest from a position in which plane of H is horizontal. The angular speed of body when plane of H is vertical is

$$\mathrm{A}\:\mathrm{rigid}\:\mathrm{body}\:\mathrm{is}\:\mathrm{made}\:\mathrm{of}\:\mathrm{three}\:\mathrm{identical} \\ $$$$\mathrm{thin}\:\mathrm{rods},\:\mathrm{each}\:\mathrm{of}\:\mathrm{length}\:{L},\:\mathrm{fastened} \\ $$$$\mathrm{together}\:\mathrm{in}\:\mathrm{the}\:\mathrm{form}\:\mathrm{of}\:\mathrm{letter}\:{H}.\:\mathrm{The} \\ $$$$\mathrm{body}\:\mathrm{is}\:\mathrm{free}\:\mathrm{to}\:\mathrm{rotate}\:\mathrm{about}\:\mathrm{a}\:\mathrm{horizontal} \\ $$$$\mathrm{axis}\:\mathrm{that}\:\mathrm{runs}\:\mathrm{along}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{legs}\:\mathrm{of}\:{H}.\:\mathrm{The}\:\mathrm{body}\:\mathrm{is}\:\mathrm{allowed}\:\mathrm{to}\:\mathrm{fall} \\ $$$$\mathrm{from}\:\mathrm{rest}\:\mathrm{from}\:\mathrm{a}\:\mathrm{position}\:\mathrm{in}\:\mathrm{which}\:\mathrm{plane} \\ $$$$\mathrm{of}\:{H}\:\mathrm{is}\:\mathrm{horizontal}.\:\mathrm{The}\:\mathrm{angular}\:\mathrm{speed} \\ $$$$\mathrm{of}\:\mathrm{body}\:\mathrm{when}\:\mathrm{plane}\:\mathrm{of}\:{H}\:\mathrm{is}\:\mathrm{vertical}\:\mathrm{is} \\ $$

Question Number 24814 Answers: 0 Comments: 3

Question Number 24786 Answers: 1 Comments: 1

A particle of mass m is moving in yz-plane with a uniform velocity v with its trajectory running parallel to +ve y- axis and intersecting z-axis at z = a. The change in its angular momentum about the origin as it bounces elastically from a wall at y = constant is : (1) mvae_x ^∧ (2) 2mvae_x ^∧ (3) ymve_x ^∧ (4) 2ymve_x ^∧

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{of}\:\mathrm{mass}\:{m}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{in}\:{yz}-\mathrm{plane} \\ $$$$\mathrm{with}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{velocity}\:{v}\:\mathrm{with}\:\mathrm{its} \\ $$$$\mathrm{trajectory}\:\mathrm{running}\:\mathrm{parallel}\:\mathrm{to}\:+\mathrm{ve}\:{y}- \\ $$$$\mathrm{axis}\:\mathrm{and}\:\mathrm{intersecting}\:{z}-\mathrm{axis}\:\mathrm{at}\:{z}\:=\:{a}. \\ $$$$\mathrm{The}\:\mathrm{change}\:\mathrm{in}\:\mathrm{its}\:\mathrm{angular}\:\mathrm{momentum} \\ $$$$\mathrm{about}\:\mathrm{the}\:\mathrm{origin}\:\mathrm{as}\:\mathrm{it}\:\mathrm{bounces}\:\mathrm{elastically} \\ $$$$\mathrm{from}\:\mathrm{a}\:\mathrm{wall}\:\mathrm{at}\:{y}\:=\:\mathrm{constant}\:\mathrm{is}\:: \\ $$$$\left(\mathrm{1}\right)\:{mva}\overset{\wedge} {{e}}_{{x}} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{2}{mva}\overset{\wedge} {{e}}_{{x}} \\ $$$$\left(\mathrm{3}\right)\:{ymv}\overset{\wedge} {{e}}_{{x}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{2}{ymv}\overset{\wedge} {{e}}_{{x}} \\ $$

Question Number 24772 Answers: 0 Comments: 13

The ratio of acceleration of points A, B and C is [assume all surfaces are smooth, pulley and strings are light]

$$\mathrm{The}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{points}\:{A}, \\ $$$${B}\:\mathrm{and}\:{C}\:\mathrm{is}\:\left[\mathrm{assume}\:\mathrm{all}\:\mathrm{surfaces}\:\mathrm{are}\right. \\ $$$$\left.\mathrm{smooth},\:\mathrm{pulley}\:\mathrm{and}\:\mathrm{strings}\:\mathrm{are}\:\mathrm{light}\right] \\ $$

Question Number 24739 Answers: 0 Comments: 12

A particle is suspended vertically from point O by ideal string of length L. It is given horizontal velocity ′v′. There is vertical line AB at a distance (L/8) from P. At some point, it leaves circular motion and follows projectile motion. At the instant it crosses AB, its velocity is horizontal. Find u

$${A}\:{particle}\:{is}\:{suspended}\:{vertically} \\ $$$${from}\:{point}\:{O}\:{by}\:{ideal}\:{string}\:{of}\:{length} \\ $$$${L}.\:{It}\:{is}\:{given}\:{horizontal}\:{velocity}\:'{v}'. \\ $$$${There}\:{is}\:{vertical}\:{line}\:{AB}\:{at}\:{a}\:{distance} \\ $$$$\frac{{L}}{\mathrm{8}}\:{from}\:{P}.\:{At}\:{some}\:{point},\:{it}\:{leaves} \\ $$$${circular}\:{motion}\:{and}\:{follows}\:{projectile} \\ $$$${motion}.\:{At}\:{the}\:{instant}\:{it}\:{crosses}\:{AB}, \\ $$$${its}\:{velocity}\:{is}\:{horizontal}.\:{Find}\:{u} \\ $$

Question Number 24730 Answers: 0 Comments: 13

Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

$$\mathrm{Consider}\:\mathrm{a}\:\mathrm{uniform}\:\mathrm{square}\:\mathrm{plate}\:\mathrm{of}\:\mathrm{side} \\ $$$${a}\:\mathrm{and}\:\mathrm{mass}\:{m}.\:\mathrm{The}\:\mathrm{moment}\:\mathrm{of}\:\mathrm{inertia} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{plate}\:\mathrm{about}\:\mathrm{an}\:\mathrm{axis}\:\mathrm{perpendicular} \\ $$$$\mathrm{to}\:\mathrm{its}\:\mathrm{plane}\:\mathrm{and}\:\mathrm{passing}\:\mathrm{through}\:\mathrm{one}\:\mathrm{of} \\ $$$$\mathrm{its}\:\mathrm{corners}\:\mathrm{is} \\ $$

Question Number 24716 Answers: 1 Comments: 0

A 2.2 kg block starts from rest on a rough inclined plane that makes an angle of 25° with the horizontal. The coefficient of kinetic friction is 0.25. As the block goes 2 m down the plane, the mechanical energy of the Earth-block system changes by

$$\mathrm{A}\:\mathrm{2}.\mathrm{2}\:\mathrm{kg}\:\mathrm{block}\:\mathrm{starts}\:\mathrm{from}\:\mathrm{rest}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{rough}\:\mathrm{inclined}\:\mathrm{plane}\:\mathrm{that}\:\mathrm{makes}\:\mathrm{an} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{25}°\:\mathrm{with}\:\mathrm{the}\:\mathrm{horizontal}.\:\mathrm{The} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:\mathrm{kinetic}\:\mathrm{friction}\:\mathrm{is}\:\mathrm{0}.\mathrm{25}.\:\mathrm{As} \\ $$$$\mathrm{the}\:\mathrm{block}\:\mathrm{goes}\:\mathrm{2}\:\mathrm{m}\:\mathrm{down}\:\mathrm{the}\:\mathrm{plane},\:\mathrm{the} \\ $$$$\mathrm{mechanical}\:\mathrm{energy}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Earth}-\mathrm{block} \\ $$$$\mathrm{system}\:\mathrm{changes}\:\mathrm{by} \\ $$

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